Tight-binding approach to penta-graphene

We introduce an effective tight-binding model to discuss penta-graphene and present an analytical solution. This model only involves the $\pi$-orbitals of the sp$^2$-hybridized carbon atoms and reproduces the two highest valence bands. By introducing energy-dependent hopping elements, originating from the elimination of the sp$^3$-hybridized carbon atoms, also the two lowest conduction bands can be well approximated - but only after the inclusion of a Hubbard onsite interaction as well as of assisted hopping terms. The eigenfunctions can be approximated analytically for the effective model without energy-dependent hopping elements and the optical absorption is discussed. We find large isotropic absorption of up to 24\% for transitions at the $\Gamma$-point, but the general absorption will show a strongly anisotropic behaviour depending on the linear polarization of the incident light.